Subgroups — #497973

Order 512.

577 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#33423	C₂	1	1	yes	maximal, characteristic, complemented
2	#33398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#443	C₂	1	1	yes	maximal, characteristic
4	#13124	C₂	1	2	yes	maximal, complemented
5	#13106	C₂	1	2	yes	maximal, complemented
6	#12980	C₂	1	2	yes	maximal
7	#12883	C₂	1	1	yes	maximal, characteristic, complemented
8	#12787	C₂	1	1	yes	maximal, characteristic, complemented
9	#12787	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#12614	C₂	1	2	yes	maximal, complemented
12	C₂×#504	C₂²	1	2	yes	—
13	C₂×#443	C₄	1	1	yes	characteristic
14	C₂×#443	C₂²	1	1	yes	characteristic
15	C₄×#135	C₄	1	1	yes	characteristic
16	C₄×#131	C₂²	1	1	yes	characteristic
17	C₄×#131	C₂²	1	1	yes	characteristic
18	#2164	—	2	2	no	—
19	#2163	—	2	1	no	—
20	#2162	—	2	1	no	—
21	#2151	—	2	2	no	—
22	#2151	C₂²	1	2	yes	—
23	#2150	—	2	1	no	—
24	#2150	C₂²	1	1	yes	characteristic
25	#2150	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₁₆	—	2	1	no	—
27	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₂×#350	C₂²	1	2	yes	—
30	C₂×#350	C₂²	1	2	yes	—
31	#2113	C₂²	1	2	yes	—
32	#2108	C₂²	1	2	yes	—
33	C₂×C₄×C₁₆	C₂²	1	2	yes	—
34	C₄×#108	C₄	1	1	yes	characteristic
35	#1772	C₄	1	1	yes	characteristic
36	#1772	C₂²	1	1	yes	characteristic
37	#1764	C₄	1	1	yes	characteristic
38	#1764	C₄	1	1	yes	characteristic
39	#1764	C₂²	1	1	yes	characteristic
40	#1764	C₂²	1	1	yes	characteristic
41	C₄×#104	C₄	1	1	yes	characteristic
42	C₄×#104	C₄	1	1	yes	characteristic
43	C₄²×C₈	C₂²	1	1	yes	characteristic
44	#1379	C₂²	1	2	yes	—
45	#1379	C₂²	1	2	yes	—
46	#1376	C₂²	1	2	yes	—
47	#1376	C₂²	1	2	yes	—
48	#1374	C₂²	1	2	yes	—
49	C₂×#135	C₂×C₄	1	1	yes	characteristic
50	C₂×#131	C₂×C₄	1	1	yes	characteristic
51	C₂×#131	C₂×C₄	1	1	yes	characteristic
52	C₂×#131	C₂³	1	1	yes	characteristic
53	C₂×#131	C₂³	1	1	yes	characteristic
54	C₄×#41	C₂×C₄	1	1	yes	characteristic
55	C₄×#41	C₂×C₄	1	1	yes	characteristic
56	#504	—	2	4	no	—
57	#504	—	4	2	no	—
58	C₂×M₃₂	—	2	2	no	—
59	C₂×M₃₂	C₂³	1	2	yes	—
60	C₂×M₃₂	C₂³	1	2	yes	—
61	C₂²×C₁₆	—	2	2	no	—
62	C₂²×C₁₆	C₂³	1	2	yes	—
63	C₂²×C₁₆	C₂³	1	2	yes	—
64	#443	—	2	2	no	—
65	#443	—	2	2	no	—
66	#443	—	2	4	no	—
67	C₄×Q₁₆	C₈	1	1	yes	characteristic
68	C₄×Q₁₆	C₈	1	1	yes	characteristic
69	C₄×SD₁₆	C₈	1	1	yes	characteristic
70	C₄×SD₁₆	C₈	1	1	yes	characteristic
71	C₄×SD₁₆	C₈	1	1	yes	characteristic
72	C₄×SD₁₆	C₈	1	1	yes	characteristic
73	C₄×D₈	C₈	1	1	yes	characteristic
74	C₄×D₈	C₈	1	1	yes	characteristic
75	C₂×#108	C₂×C₄	1	1	yes	characteristic
76	C₂×#108	C₂×C₄	1	1	yes	characteristic
77	#427	C₂×C₄	1	1	yes	characteristic
78	C₂×#104	C₂×C₄	1	1	yes	characteristic
79	C₂×#104	C₂×C₄	1	1	yes	characteristic
80	C₂×#104	C₂×C₄	1	1	yes	characteristic
81	C₂×#104	C₂×C₄	1	1	yes	characteristic
82	#416	C₂×C₄	1	1	yes	characteristic
83	#416	C₂×C₄	1	1	yes	characteristic
84	#405	—	2	1	no	—
85	#405	—	2	1	no	—
86	#405	—	2	1	no	—
87	#405	—	2	1	no	—
88	#405	C₂×C₄	1	1	yes	characteristic
89	#405	C₂×C₄	1	1	yes	characteristic
90	#405	C₂³	1	1	yes	characteristic
91	#405	C₂³	1	1	yes	characteristic
92	C₄×M₁₆	—	2	1	no	—
93	C₄×M₁₆	—	2	1	no	—
94	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
95	C₄×M₁₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×C₈	—	2	1	no	—
97	C₂×C₄×C₈	—	2	1	no	—
98	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄×C₈	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₄×C₈	C₂³	1	1	yes	characteristic
104	C₄³	C₂×C₄	1	1	yes	characteristic
105	C₄⋊C₁₆	—	2	2	no	—
106	C₄⋊C₁₆	—	2	2	no	—
107	C₄⋊C₁₆	—	2	1	no	—
108	C₄⋊C₁₆	—	2	1	no	—
109	C₄⋊C₁₆	—	2	1	no	—
110	C₄⋊C₁₆	—	2	1	no	—
111	C₄⋊C₁₆	—	2	1	no	—
112	C₄⋊C₁₆	—	2	1	no	—
113	C₄⋊C₁₆	D₄	1	1	yes	characteristic
114	C₄⋊C₁₆	D₄	1	1	yes	characteristic
115	C₄⋊C₁₆	D₄	1	2	yes	—
116	#350	—	2	4	no	—
117	#350	—	4	2	no	—
118	C₂²⋊C₁₆	—	2	2	no	—
119	C₂²⋊C₁₆	—	2	2	no	—
120	#346	—	2	2	no	—
121	C₄×C₁₆	—	2	2	no	—
122	C₄×C₁₆	—	4	2	no	—
123	#341	C₂×C₄	1	1	yes	characteristic
124	#341	C₂×C₄	1	1	yes	characteristic
125	#339	C₂×C₄	1	1	yes	characteristic
126	#339	C₂×C₄	1	1	yes	characteristic
127	#339	C₂×C₄	1	1	yes	characteristic
128	#339	C₂×C₄	1	1	yes	characteristic
129	C₂×#41	C₂²×C₄	1	1	yes	characteristic
130	C₂×#41	C₂²×C₄	1	1	yes	characteristic
131	#135	—	2	2	no	—
132	#135	—	2	2	no	—
133	C₂×Q₁₆	C₂×C₈	1	1	yes	characteristic
134	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
135	C₂×SD₁₆	C₂×C₈	1	1	yes	characteristic
136	C₂×D₈	C₂×C₈	1	1	yes	characteristic
137	#131	—	2	1	no	—
138	#131	—	2	1	no	—
139	#131	—	2	2	no	—
140	#131	—	2	2	no	—
141	#131	—	2	1	no	—
142	#131	—	2	1	no	—
143	#131	—	2	1	no	—
144	#131	—	2	1	no	—
145	#131	—	4	1	no	—
146	#131	—	4	1	no	—
147	#131	#41	1	2	yes	—
148	#131	#41	1	2	yes	—
149	C₂×M₁₆	—	2	1	no	—
150	C₂×M₁₆	—	2	1	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	—	2	1	no	—
153	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
154	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
155	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
156	C₂×M₁₆	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₈	—	2	1	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	2	1	no	—
160	C₂²×C₈	—	2	1	no	—
161	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₈	C₂⁴	1	1	yes	characteristic
165	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
166	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
167	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
168	C₄×Q₈	C₂×C₈	1	1	yes	characteristic
169	C₄×D₄	—	2	1	no	—
170	C₄×D₄	—	2	1	no	—
171	C₄×D₄	—	2	1	no	—
172	C₄×D₄	—	2	1	no	—
173	C₄×D₄	C₂×C₈	1	1	yes	characteristic
174	C₄×D₄	C₂×C₈	1	1	yes	characteristic
175	C₄×D₄	C₂×C₈	1	1	yes	characteristic
176	C₄×D₄	C₂×C₈	1	1	yes	characteristic
177	#117	—	2	1	no	—
178	#117	—	2	1	no	—
179	#117	C₂²×C₄	1	1	yes	characteristic
180	#117	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄²	—	2	1	no	—
182	C₂×C₄²	—	2	1	no	—
183	C₂×C₄²	—	2	1	no	—
184	C₂×C₄²	—	2	1	no	—
185	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₄²	C₂²×C₄	1	1	yes	characteristic
188	M₃₂	—	2	2	no	—
189	M₃₂	—	2	2	no	—
190	M₃₂	—	2	2	no	—
191	M₃₂	—	2	2	no	—
192	M₃₂	—	4	4	no	—
193	C₂×C₁₆	—	2	2	no	—
194	C₂×C₁₆	—	2	2	no	—
195	C₂×C₁₆	—	2	2	no	—
196	C₂×C₁₆	—	2	2	no	—
197	C₂×C₁₆	—	2	2	no	—
198	C₂×C₁₆	—	2	2	no	—
199	C₂×C₁₆	—	2	2	no	—
200	C₂×C₁₆	—	4	4	no	—
201	C₂×C₁₆	C₂×D₄	1	2	yes	—
202	C₂×C₁₆	C₂×D₄	1	2	yes	—
203	#108	—	2	2	no	—
204	#108	—	2	2	no	—
205	#107	C₂×C₈	1	1	yes	characteristic
206	#107	C₂×C₈	1	1	yes	characteristic
207	#106	C₂×C₈	1	1	yes	characteristic
208	#106	C₂×C₈	1	1	yes	characteristic
209	#104	—	2	2	no	—
210	#104	—	2	2	no	—
211	#104	—	2	2	no	—
212	#104	M₁₆	1	4	yes	—
213	#103	C₂×C₈	1	1	yes	characteristic
214	#103	C₂×C₈	1	1	yes	characteristic
215	#103	C₂×C₈	1	1	yes	characteristic
216	#103	C₂×C₈	1	1	yes	characteristic
217	#102	C₂×C₈	1	1	yes	characteristic
218	#102	C₂×C₈	1	1	yes	characteristic
219	#102	C₂×C₈	1	1	yes	characteristic
220	#102	C₂×C₈	1	1	yes	characteristic
221	#97	—	2	1	no	—
222	#97	—	2	1	no	—
223	#97	—	2	1	no	—
224	#97	—	2	1	no	—
225	#97	—	2	1	no	—
226	#97	—	2	1	no	—
227	C₄×C₈	—	2	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	2	1	no	—
230	C₄×C₈	—	2	1	no	—
231	C₄×C₈	—	2	1	no	—
232	C₄×C₈	—	2	1	no	—
233	C₄×C₈	—	2	1	no	—
234	C₄×C₈	—	2	1	no	—
235	C₄×C₈	—	2	1	no	—
236	C₄×C₈	—	2	1	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	—	4	1	no	—
239	C₄×C₈	C₂×C₈	1	1	yes	characteristic
240	C₄×C₈	C₂×C₈	1	1	yes	characteristic
241	C₄×C₈	C₂×C₈	1	1	yes	characteristic
242	C₄×C₈	C₂×C₈	1	1	yes	characteristic
243	C₄×C₈	C₂×D₄	1	1	yes	characteristic
244	C₄×C₈	C₂×D₄	1	1	yes	characteristic
245	C₄×C₈	#41	1	1	yes	characteristic
246	C₄×C₈	#41	1	1	yes	characteristic
247	#41	—	2	1	no	—
248	#41	—	2	1	no	—
249	#41	—	2	1	no	—
250	#41	—	2	1	no	—
251	#41	—	2	1	no	—
252	#41	—	2	1	no	—
253	#41	#117	1	2	yes	—
254	#41	C₂×M₁₆	1	2	yes	—
255	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
256	C₂×Q₈	C₂²×C₈	1	1	yes	characteristic
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
260	C₂×D₄	C₂²×C₈	1	1	yes	characteristic
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	#131	1	1	yes	characteristic
270	C₂²×C₄	#131	1	1	yes	characteristic
271	C₂²×C₄	C₂³×C₄	1	1	yes	characteristic
272	Q₁₆	—	2	2	no	—
273	SD₁₆	—	2	2	no	—
274	SD₁₆	—	2	2	no	—
275	D₈	—	2	2	no	—
276	M₁₆	—	2	1	no	—
277	M₁₆	—	2	1	no	—
278	M₁₆	—	2	2	no	—
279	M₁₆	—	2	2	no	—
280	M₁₆	—	2	1	no	—
281	M₁₆	—	2	1	no	—
282	M₁₆	—	2	1	no	—
283	M₁₆	—	2	1	no	—
284	M₁₆	—	4	2	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	4	1	no	—
287	M₁₆	—	4	1	no	—
288	M₁₆	#117	1	2	yes	—
289	M₁₆	C₂×M₁₆	1	2	yes	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	C₄×D₄	1	1	yes	characteristic
307	C₂×C₈	C₄×D₄	1	1	yes	characteristic
308	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
309	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
310	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
311	C₂×C₈	C₂²×C₈	1	1	yes	characteristic
312	C₂×C₈	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂×#41	1	1	yes	characteristic
314	C₂×C₈	C₂×#41	1	1	yes	characteristic
315	C₂×C₈	C₂×#41	1	1	yes	characteristic
316	C₂×C₈	H(5,𝔽₂)	1	1	yes	characteristic
317	C₂×C₈	2₋¹⁺⁴	1	1	yes	characteristic
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
323	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
324	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
325	C₄⋊C₄	C₂²×C₈	1	1	yes	characteristic
326	C₂²⋊C₄	—	2	1	no	—
327	C₂²⋊C₄	—	2	1	no	—
328	C₂²⋊C₄	—	2	1	no	—
329	C₂²⋊C₄	—	2	1	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	4	2	no	—
343	C₄²	C₄×D₄	1	1	yes	characteristic
344	C₄²	C₄×D₄	1	1	yes	characteristic
345	C₄²	C₂²×C₈	1	1	yes	characteristic
346	C₄²	C₂²×C₈	1	1	yes	characteristic
347	C₄²	C₂×M₁₆	1	2	yes	—
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	2	no	—
350	C₁₆	—	4	2	no	—
351	C₁₆	—	4	2	no	—
352	C₁₆	—	4	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	C₂×#131	1	1	yes	characteristic
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	2	1	no	—
359	Q₈	#431	1	2	yes	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	#431	1	2	yes	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	C₈×D₄	1	1	yes	characteristic
391	C₂×C₄	C₈×D₄	1	1	yes	characteristic
392	C₂×C₄	C₈×D₄	1	1	yes	characteristic
393	C₂×C₄	C₈×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×#117	1	1	yes	characteristic
395	C₂×C₄	C₂×C₄×D₄	1	1	yes	characteristic
396	C₂×C₄	#520	1	1	yes	characteristic
397	C₂×C₄	C₂³×C₈	1	1	yes	characteristic
398	C₂×C₄	C₂²×M₁₆	1	1	yes	characteristic
399	C₂×C₄	#568	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	#546	1	1	yes	characteristic
411	C₈	#548	1	1	yes	characteristic
412	C₈	#552	1	1	yes	characteristic
413	C₈	#553	1	1	yes	characteristic
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	#2925	1	1	yes	characteristic
423	C₂²	C₂×C₈×D₄	1	1	yes	characteristic
424	C₂²	#2990	1	1	yes	characteristic
425	C₄	—	2	4	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	4	1	no	—
436	C₄	#2170	1	2	yes	—
437	C₄	#2352	1	1	yes	characteristic
438	C₄	C₂×#431	1	1	yes	characteristic
439	C₄	D₄×M₁₆	1	1	yes	characteristic
440	C₄	#2988	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	4	2	no	—
444	C₂	—	8	1	no	—
445	C₂	#22748	1	1	yes	characteristic
446	C₂	C₂×#2170	1	1	yes	characteristic
447	C₂	#33443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×D₄
commutator	C₂×C₄	C₂³×C₈
Frattini, cosocle	C₂²×C₈	C₂⁴
socle	C₂²	C₂×C₈×D₄
prime radical	C₂×#135	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄⋊C₁₆ ◁ G
LECS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #33423	C₂	semidirect
2. #33398	C₂	semidirect
4. #13124	C₂	semidirect
5. #13106	C₂	semidirect
7. #12883	C₂	semidirect
8. #12787	C₂	semidirect
9. #12787	C₂	semidirect
10. C₄×C₄⋊C₁₆	C₂	semidirect
11. #12614	C₂	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#33423	2
#33398	2
C₄×#443	2
#13124	2
#13106	2
#12980	2
#12883	2
#12787	2
C₄×C₄⋊C₁₆	2
#12614	2